godot/thirdparty/thekla_atlas/nvmath/ConvexHull.cpp

// This code is in the public domain -- Ignacio Casta<74>o <castano@gmail.com>

#include "ConvexHull.h"

#include "Vector.inl"

#include "nvcore/RadixSort.h"
#include "nvcore/Array.inl"

using namespace nv;

inline static float triangleArea(Vector2::Arg v1, Vector2::Arg v2, Vector2::Arg v3)
{
    return 0.5f * (v3.x * v1.y + v1.x * v2.y + v2.x * v3.y - v2.x * v1.y - v3.x * v2.y - v1.x * v3.y);
}


// Compute the convex hull using Graham Scan.
void nv::convexHull(const Array<Vector2> & input, Array<Vector2> & output, float epsilon/*=0*/)
{
    const uint inputCount = input.count();

    Array<float> coords;
    coords.resize(inputCount);

    for (uint i = 0; i < inputCount; i++) {
        coords[i] = input[i].x;
    }

    RadixSort radix;
    radix.sort(coords);

    const uint * ranks = radix.ranks();

    Array<Vector2> top(inputCount);
    Array<Vector2> bottom(inputCount);

    Vector2 P = input[ranks[0]];
    Vector2 Q = input[ranks[inputCount-1]];

    float topy = max(P.y, Q.y);
    float boty = min(P.y, Q.y);

    for (uint i = 0; i < inputCount; i++) {
        Vector2 p = input[ranks[i]];
        if (p.y >= boty) top.append(p);
    }

    for (uint i = 0; i < inputCount; i++) {
        Vector2 p = input[ranks[inputCount-1-i]];
        if (p.y <= topy) bottom.append(p);
    }

    // Filter top list.
    output.clear();
    output.append(top[0]);
    output.append(top[1]);

    for (uint i = 2; i < top.count(); ) {
        Vector2 a = output[output.count()-2];
        Vector2 b = output[output.count()-1];
        Vector2 c = top[i];

        float area = triangleArea(a, b, c);

        if (area >= -epsilon) {
            output.popBack();
        }

        if (area < -epsilon || output.count() == 1) {
            output.append(c);
            i++;
        }
    }
    
    uint top_count = output.count();
    output.append(bottom[1]);

    // Filter bottom list.
    for (uint i = 2; i < bottom.count(); ) {
        Vector2 a = output[output.count()-2];
        Vector2 b = output[output.count()-1];
        Vector2 c = bottom[i];

        float area = triangleArea(a, b, c);

        if (area >= -epsilon) {
            output.popBack();
        }

        if (area < -epsilon || output.count() == top_count) {
            output.append(c);
            i++;
        }
    }

    // Remove duplicate element.
    nvDebugCheck(output.front() == output.back());
    output.popBack();
}

/*
void testConvexHull() {

    Array<Vector2> points;
    points.append(Vector2(1.00, 1.00));
    points.append(Vector2(0.00, 0.00));
    points.append(Vector2(1.00, 1.00));
    points.append(Vector2(1.00, -1.00));
    points.append(Vector2(2.00, 5.00));
    points.append(Vector2(-5.00, 3.00));
    points.append(Vector2(-4.00, -3.00));
    points.append(Vector2(7.00, -4.00));

    Array<Vector2> hull;
    convexHull(points, hull);

}
*/